Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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Chapter 27, Problem 98P
(a)
To determine
The expression for magnetic field at a point of the
(b)
To determine
The proof that for
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Given a magnetic vector potential A = 3ρe-z aφ, what is the magnetic flux through the surface z = -5, 0 < ρ < 3?
The magnetic field B due to a small current loop (which is placed at the origin) is called a magnetic dipole. Let
p = (x² + y² + z²)¹/² For p large, B = curl(A), where
A = (-33, -3,0)
R
Current loop
(a) Let C be a horizontal circle of radius R with center (0, 0, c), and parameterization c(t) where c is large.
Which of the following correctly explains why A is tangent to C?
A(c(t)) =
So, A(c(t)) =
A(c(t))
-(-²
A(c(t)) =
=
A(c(t))
cos(0,0)
p3
(1). Therefore, A is parallel to c'(t) and tangent to C.
Rcos(t) R sin(t)
= (-OS
R sin(t) R cos(1)
p³
So, A(c(1)) = -c'(1). Therefore, A is parallel to c'(t) and tangent to C.
O
BdS =
=
and c'(t)= (-R sin(t), R cos(t), 0)
Rin(1,0) and c'(t) = (R cos(1), -R sin(1), 0)
So, A(c(t)) c(t) = 0. Therefore, A is perpendicular to c'(t) and tangent to C.
O
R sin(1) R cos(1)
(R$ R COS(0,0) and c'(t) = (R cos(t), - R sin(t), 0)
R cos(1)
p3
So, A(c(t)) - c'(t) = 0. Therefore, A is perpendicular to c' (t) and tangent to C.
R sin(t)
-
and c'(t)= (-R sin(t), R…
The current in a long, straight conductor has the following form:I(t) = I0cos ωtWhat is the magnitude of the magnetic field a distance r away from theconductor?
Chapter 27 Solutions
Physics for Scientists and Engineers
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